Discussion on some FFT problems to determine the geoid

The aim of this investigation is to study some FFT problems related to the application of FFT to gravity field convolution integrals. And the others, such as the effect of spectral leakage, edge effects, cyclic convolution and effect of padding, are also discussed. A numerical test for these problems is made. A large area of Western China selected for the test is located between 30°N～36°N and 96°E～102°E and includes 1 858 gravity observations on land. The results show that the removal of the bias in the residual gravity anomalies is important to avoid spectral leakage. One hundred percent zero padding is highly recommended for further research of the geoid to remove cyclic convolution errors and edge effects. 1-D FFT is recommended for precise local geoid determination because it does not use kernel approximation.     

Time-fractional Burgers equation for dust acoustic waves in a two different temperatures dusty plasma

The reductive perturbation method has been used to derive the Burgers equation for dust acoustic shock waves in unmagnetized plasma having electrons, singly charged ions, hot and cold dust species with Boltzmann distributions for electrons and ions in the presence of the cold (hot) dust viscosity coefficients. The time-fractional Burgers equation is formulated using Euler-Lagrange variational technique and is solved using the variational-iteration method. The effect of time fractional parameter on the behavior of the shock waves in the dusty plasma has been investigated.     

The microwave opacity of Saturn's rings at wavelengths of 3.6 and 13 cm from Voyager 1 radio occultation

Radio occultation observations of Saturn's rings with Voyager 1 provided independent measurements of complex (amplitude and phase) microwave extinction and near-forward scattering cross section of the rings at wavelengths (λ) of 3.6 and 13 cm. The ring opening was 5.9°. The normal microwave opacities, τ[3.6] and τ[13], provide a measure of the total cross-sectional area of particles larger than about 1 and 4 cm radius, respectively. Ring C exhibits gently undulating (～ 1000 km) structure of normal opacity τ[3.6] ? 0.25 except for several narrow imbedded ringlets of less than about 100 km width and τ[3.6] ～ 0.5 to 1.0. The normalized differential opacity Δτ/τ[3.6], where Δτ = τ[3.6] ? τ[13], is about 0.3 over most of ring C, indicating a substantial fraction of centimeter-size particles. Some narrow imbedded ringlets show marked increases in Δτ/τ[3.6] near their edges, implying an enhancement in the relative population of centimeter-size and smaller particles at those locations. In the Cassini division, several sharply defined gaps separate regions of opacity τ ～ 0.08 and τ ～ 0.25; the opacity in the Cassini Division appears to be nearly independent of λ. The boundary features at the outer edges of ring C and the Cassini Division are remarkably similar in width and opacity profile, suggesting a similar dynamical control. Ring A appears to be nearly homogeneous over much of its width with 0.6 < τ[3.6] < 0.8 but with considerable thickening, to τ[3.6] ～ 1.0, near its inner boundary with the Cassini division. Normalized differential opacity decreases from ～0.3 at the inner and outer edges of ring A to Δτ/τ[3.6] ～ 0 at a point about one-third of the distance from the inner edge to the outer. The inner one-fourth of ring B has τ[3.6] ～ 1.0, except very near the boundary with ring C, where it is greater. The outer three-fourths of ring B has $\text{τ[3.6] ? 1.2}$. The differential opacity for the inner one-fourth of ring B is Δτ/τ[3.6] ～ 0.15. There are no gaps in ring B exceeding about 2 km in width. Ring F was observed at 3.6 cm as a single ringlet of radial width $\text{? 2}\text{km}$, but was not detected in 13 cm data.     

Models for Fitting Gravimetric Geoids and GPS Results

The aim of this investigation is to study how to use a gravimetric(quasi) geoid for levelling by GPS data in an optimal way.The advent of precise geodetic GPS has made the use of a technique possible,which might be called GPS- gravimetric geoid determination.In this approach,GPS heights above the reference ellipsoid are determined for points whose levelled (orthometric) height H is above sea level people have already surveyed;for these points,we thus have the values of the geoid undulation N.These values are then used to constrain the geoid undulations N‘ obtained from the gravimetric solution.     

Mineralogical and geochemical studies on Egyptian (U.A.R.) black sands

The economic mineral constituents of the black sand deposits occurring at the outpourings of the Nile Delta, Egypt, were studied from the mineralogical and geochemical point of view. These include magnetite, ilmenite, zircon, monazite, rutile und garnet. Microscopical, X-ray, chemical und spectrographic analyses are reported and discussed for each mineral.

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Zusammenfassung Die wirtschaftlich wichtigen Mineralkomponenten der Schwarzsand-Ablagerungen, die an den Mündungen des Nildeltas in Ägypten vorkommen, wurden in mineralogischer und geochemischer Hinsicht untersucht. Sie enthalten Magnetit, Ilmenit, Zirkon, Monazit, Rutil und Granat. Mikroskopische, röntgenographische, chemische und spektrographische Analysen werden für jedes Mineral angeführt und diskutiert.

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With 9 Figures in the Text     

Economic evaluation of using marine dredged material for erosion control along the northeast coast of the Nile Delta,Egypt

The present study is the first attempt in Egypt to assess feasibility of using of dredging material from Damietta Harbor in the northwestern Nile Delta for erosion control. The study also provides an economic evaluation for the shoreline management alternatives selected to mitigate for the effects of coastal erosion at two pilot eroding areas (namely, A and B) located near the Damietta Harbor. Results of compatibility analysis reveal that the dredging material is fairly compatible with the native sand of the nearby eroding beaches. In addition to soft nourishment by dredged sand, other types of coastal engineering measures which are often used in erosion management area were also evaluated as alternatives for erosion control and mitigation solution. Economic feasibility assessment by means of cost-benefit analysis of direct and indirect items has been carried out to facilitate comparison between these alternatives. Analysis of alternatives has been also supported by other criteria to select the cost-effective and environmentally acceptable option to protect the eroding pilot areas. These criteria include the high total cost paid for maintenance of the Damietta Harbor channel with no use, anticipated impacts on the littoral system, sustainability, future plans for protection of the existing coastlines, and lessons learned from previous shore protection works in the Nile Delta. The final selection of the best viable alternative indicates that the procedure of beach nourishment is the most appropriate form for protection area A, while a combination of groins and sand nourishment is more relevant for area B. In any case, material dredged from the navigation approach of the Damietta Harbor should be utilized as a borrow material in the nourishment schemes and excluding use of the terrestrial sources.     

Study the feasibility of using PPP for establishing CORS network

Nowadays many continuously operating reference stations (CORS) network were established in Middle East to improve the surveying tasks. Establishing such geodetic control networks can be a costly business where multiple stations should be occupied simultaneously and post-processed with scientific software. Recently, precise point positioning (PPP) provides precise positioning values that may be an alternative to precise relative processing. The current research aims to investigate that PPP has a potential as a reliable absolute positioning technique operational simplicity as well as to investigate the capability of PPP approach to be a low cost alternative to the conventional positioning methods used in position determination of core networks stations. In comparison with common relative GPS techniques, the costs are reduced; because no base stations and no simultaneous observations are necessary, no need for control network maintenance which could be the most defective factors that Egypt HARN network suffered from. To see the feasibility study of using PPP for precise determination of the CORS, 14 days of GNSS data for the 14 Kuwait integrated with 27 IGS stations were processed by Bernese software to calculate the precise coordinates of Kuwaiti CORS network in the latest terrestrial geodetic frame. Three days of these data were processed by Trimble business center software and using PPP approach to calculate the precise coordinates of Kuwait network. In the current research, a comparable investigation was carried out between the coordinates obtained from Bernese software, Trimble business center, and PPP approach. The comparison proved high level of agreement between the coordinates which confirm that PPP approach can be applied for establishment of CORS network.     

Remarks on “biaxial” calcite

Biaxial calcite grains occur in several Egyptian carbonate rocks. The degree of biaxiality is nearly consistent; the optic axial angle being in the range of 8–10°. The reasons of this “biaxiality” are discussed and it is urged that this phenomenon should be considered both in research and teaching.     

Geochemistry of ground waters from some localities West of the Nile Delta

The geochemistry of ground waters from Tahrir Province and Wadi El-Natrun, both West of the Nile Delta, has been studied in detail. The distribution of cations and anions in the water shows that the concentration of calcium and magnesium is lower in Wadi El-Natrun than in Tahrir, while sodium, carbonate and bicarbonate and chloride ions are higher. The concentration of potassium and sulphate ions is identical.The regional variations in the chemistry of the ground waters have been studied in detail using iso-concentration maps of both cations and anions. The trends of variation from the Nile Delta towards Wadi El-Natrun are characterized by an increase in the salinity and hence an increase in the concentration of most anions and cations.Using Collins bar graphs, the relationships between cations and anions and the salt assemblages encountered in the waters are outlined.The ground waters of Tahrir and Wadi El-Natrun are classified as recycled, good potable to fresh waters. They belong mainly to the sodium bicarbonate and Ca-Mg bicarbonate classes. The seasonal changes in the composition of the water have been studied in detail over a period of about one year.

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Zusammenfassung Diese Arbeit beschäftigt sich mit der Geochemie der Grundwässer der Tahrir-Provinz und des Gebietes des Wadi El-Natrun, westlich vom Nildelta.Die Verteilung der Kationen und Anionen in diesen Wässern zeigt, daß der Gehalt an Kalzium und Magnesium niedriger, dagegen der Gehalt an Natrium-, Karbonat- und Chloridionen höher im Gebiet des Wadi El-Natrun, als in der Tahrir-Provinz ist. Kalium- und Sulfat-Gehalte sind identisch.Die regionalen Unterschiede im Chemismus der Grundwässer wurde mit Hilfe der Iso-Konzentrationskarte von Kationen und Anionen untersucht. Vom Nildelta bis Wadi El-Natrun wird eine zunehmende Tendenz der Salinität bzw. der meisten Kationen und Anionen festgestellt.Es wird der Zusammenhang zwischen Anionen und Kationen und die Salzzusammensetzung der Wässer beschrieben. Die Grundwässer der Tahrir-Provinz und des Wadi El-Natrun sind genetisch als Kreislaufwässer zu betrachten. Sie besitzen überwiegend eine Natrium-Bikarbonat- und Kalzium-Magnesium-Bikarbonat-Vormacht. Im Laufe eines Jahres wurden die periodisch auftretenden Unterschiede im Chemismus der Wässer von Tahrir und Wadi El-Natrun gründlich untersucht.

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Résumé Ce travail a pour but l'étude de la géochimie des eaux souterraines dans la province de Tahrir et dans la région de Wadi El-Natrum (Egypte), à l'W du delta du Nil. La répartition des cations et des anions dans ces eaux montre que la teneur en Ca et Mg est plus faible, et celle en Na, carbonates et chloride, plus élevée, dans la région de Wadi El-Natrum que dans la province de Tahrir. Les teneurs en K et en sulfates sont identiques.Les différences régionales dans la composition chimique des eaux souterraines ont été évaluées à l'aide de cartes d'isoconcentrations de cations et d'anions.Du delta du Nil jusque Wadi El-Natrum, la salinité tend à augmenter. L'auteur exprime le caractère unitaire existant entre les anions et cations et la composition des sels. Les eaux de Tahrir et de Wadi El-Natrun sont des eaux météoriques. Elles possèdent de façon prédominante du bicarbonate de Na et du bicarbonate de Ca-Mg. Les différences de chimisme périodiques qu'elles subissent au cours d'une année ont été étudiées.

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